江苏省应用数学（中国矿业大学）中心系列学术报告
报告题目：Explicit potential function and fast algorithm for computing potentials in α×β conic surface resistor network
时 间：2023年10月 16 日（星期 一 ），下午 3：30-4：30
地 点：中国矿业大学应用数学中心（数学学院A321）
主 办：中国矿业大学数学学院
参加对象：感兴趣的老师和研究生
报告摘要：Resistor network research is of great importance, yet many resistor networks and their large-scale fast computations have not received sufficient attention. This talk proposes a new resistor network with idiosyncratic shape, i.e., a α× β conic surface resistor network that resembles the upper part of a three-dimensional Dirac function. Utilizing the Recursion Transform (RT-V) method, a recursive matrix equation model is constructed based on Kirchhoff’s law and nodal voltages, which contains the modified tridiagonal Toeplitz matrix. By using the orthogonal matrix transformation, the eigenvalues and eigenvectors of the modified tridiagonal Toeplitz are obtained. The discrete sine transform of the fourth type (DST-IV) is utilized to solve node voltages, while the explicit potential function is represented by the Chebyshev polynomials of the second kind. In addition, explicit potential functions for some special cases are provided, and the potential distribution is illustrated using dynamic three-dimensional graph. To achieve a rapid calculation of the potential, a fast algorithm based on the multiplication of DST-IV with a vector is proposed. In the end, analysis of computational efficiency for the explicit potential function and the fast algorithm are shown.
报告人简介：江兆林，现任临沂大学数学与科学计算研究所所长，校特聘二级教授、首批沂蒙学者特聘教授、博士生导师，曾任理学院院长、数学与统计学院院长等。山东省中青年学术骨干，山东省首届教指委成员、美国数学会评论员、中国线性代数学会副秘书长、中国运筹学会线性规划分会理事。在 Physical Review E、Sci China Math、Applied Mathematics and Computation、Linear Algebra and its Applications、Journal of Computational Mathematics、Scientific Reports、IET Signal Processing等60余种国内外学术期刊发表学术论文160余篇，其中SCI检索65篇。出版专著一部，主编、主审高校教材10多部, 主编、主审数学教育类读物8部。先后主持或参与了国家级、省级等课题19项。先后出访过10个国家（地区）的60多所大学（如：牛津大学、剑桥大学、哈佛大学、斯坦福大学、东京大学、名古屋大学、洪堡大学、巴黎高师、首尔大学、台湾大学、香港中文大学、香港理工大学、莫斯科大学、圣彼得堡国立技术大学等）。主要从事图象处理、电阻网络、神经网络、机器人路径规划、特殊矩阵的理论、算法及其应用、数值代数等方面的研究工作。